1.

Circuitry implementation of a novel nonautonomous hyperchaotic Liu system based on sine input





罗小华《中国物理 B》,2009年第18卷第8期


Based on the threedimensional Liu system with a nonlinear term of square,this paper appends a state variable to the system,and further adds a driving signal of the sine signal to construct a novel 4demensional nonautonomous hyperchaotic Liu system.The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal.Through adjusting the frequency of the driving signal,the system can be controlled to show some different dynamic behaviors.By numerical simulations,the Lyapunov exponent spectrums,bifurcation diagrams and phase diagrams of the novel systems are analyzed.Furthermore,the corresponding hardware circuits are implemented.Both the experimental results and the simulation results confirm that the method is feasible.The method,which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors,can make the dynamic property of the system become more complex,but easier to be controlled accurately as well.

2.

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 被引次数：1





汪浩祥 蔡国梁 缪盛 田立新《中国物理 B》,2010年第19卷第3期


This paper reports a new hyperchaotic system by adding an additional state variable into a threedimensional chaotic dynamical system.Some of its basic dynamical properties,such as the hyperchaotic attractor,Lyapunov exponents,bifurcation diagram and the hyperchaotic attractor evolving into periodic,quasiperiodic dynamical behaviours by varying parameter k are studied.An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium.Furthermore,a circuit is designed to realize this new hyperchaotic system by electronic workbench(EWB).Numerical simulations are presented to show these results.

3.

A new hyperchaotic system and its linear feedback control 被引次数：1





蔡国梁 郑 松 田立新《中国物理 B》,2008年第17卷第11期


This paper reports a new hyperchaotic system by adding an additional state variable into a threedimensional chaotic dynamical system, studies some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasiperiodic dynamical behaviours by varying parameter k. Furthermore, effective linear feedback control method is used to suppress hyperchaos to unstable equilibrium, periodic orbits and quasiperiodic orbits. Numerical simulations are presented to show these results.

4.

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal





卢俊国《中国物理》,2006年第15卷第1期


This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scaledriving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the RSssler hyperchaotic systems and Chua＇s chaotic oscillators.

5.

Synchronization and parameter identification of one class of realistic chaotic circuit





王春妮 马军 褚润通 李世荣《中国物理 B》,2009年第18卷第9期


In this paper,the synchronization and the parameter identification of the chaotic PikovskyRabinovich(PR) circuits are investigated.The linear error of the second corresponding variables is used to change the driven chaotic PR circuit,and the complete synchronization of the two identical chaotic PR circuits is realized with feedback intensity k increasing to a certain threshold.The Lyapunov exponents of the chaotic PR circuits are calculated by using different feedback intensities and our results are confirmed.The case where the two chaotic PR circuits are not identical is also investigated.A general positive Lyapunov function V,which consists of all the errors of the corresponding variables and parameters and changeable gain coefficient,is constructed by using the Lyapunov stability theory to study the parameter identification and complete synchronization of two nonidentical chaotic circuits.The controllers and the parameter observers could be obtained analytically only by simplifying the criterion dV/dt < 0(differential coefficient of Lyapunov function V with respect to time is negative).It is confirmed that the two nonidentical chaotic PR circuits could still reach complete synchronization and all the unknown parameters in the drive system are estimated exactly within a short transient period.

6.

A new hyperchaos system and its circuit simulation by EWB





周平 曹玉霞 程雪峰《中国物理 B》,2009年第18卷第4期


This paper reports a new hyperchaotic system evolved from the threedimensional L chaotic system. The Lyapunov exponents spectrum and the bifurcation diagram of this new hyperchaotic system are obtained. Hyperchaotic attractor, periodic orbit and chaotic attractor are obtained by computer simulation. A circuit is designed to realize this new hyperchaotic system by electronic workbench.

7.

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system





王繁珍 陈增强 吴文娟 袁著祉《中国物理》,2007年第16卷第11期


This paper reports a new fourdimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the fourdimensional system can evolve into periodic, quasiperiodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.[第一段]

8.

Adaptive synchronization of hyperchaotic Lü system with uncertainty 被引次数：1





高秉建 陆君安《中国物理》,2007年第16卷第3期


This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed for the synchronization of hyperchaotic Lfi systems with uncertainty. Numerical simulations are given to demonstrate the validity of the synchronization technique.

9.

Adaptive synchronization of hyperchaotic Lü system with uncertainty





高秉建 陆君安《中国物理》,2007年第16卷第3期


This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed for the synchronization of hyperchaotic Lfi systems with uncertainty. Numerical simulations are given to demonstrate the validity of the synchronization technique.

10.

A single adaptive controller with one variable for synchronization of fractionalorder chaotic systems





张若洵 杨世平《中国物理 B》,2012年第21卷第8期


In this paper we investigate the synchronization of a class of threedimensional fractionalorder chaotic systems.Based on the Lyapunov stability theory and adaptive control technique,a single adaptivefeedback controller is developed to synchronize a class of fractionalorder chaotic systems.The presented controller which only contains a single driving variable is simple both in design and in implementation.Numerical simulation and circuit experimental results for fractionalorder chaotic system are provided to illustrate the effectiveness of the proposed scheme.

11.

Projective synchronization of a hyperchaotic system via periodically intermittent control





黄军建 李传东 张伟 韦鹏程《中国物理 B》,2012年第9期


We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.

12.

Chaotic synchronization via linear controller





陈凤祥 张卫东《中国物理》,2007年第16卷第4期


A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascadeconnected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.

13.

A novel mixedsynchronization phenomenon in coupled Chua’s circuits via nonfragile linear control





王军威 马庆华 曾丽《中国物理 B》,2011年第20卷第8期


Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme.In this paper,a nonfragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixedsynchronization of Chua’s circuits connected in a driveresponse configuration.In particular,in the mixedsynchronization regime,different state variables of the response system can evolve into complete synchronization,antisynchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix.Using Lyapunov stability theory,we derive some sufficient criteria for achieving global mixedsynchronization.It is shown that the desired nonfragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs).Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.

14.

Synchronization of the fractionalorder generalized augmented L u¨system and its circuit implementation





薛薇 徐进康 仓诗建 贾红艳《中国物理 B》,2014年第6期


In this paper, the synchronization of the fractionalorder generalized augmented Lu¨ system is investigated. Based on the predictor–corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincare′maps of the fractionalorder system and find that a fourwing chaotic attractor exists in the system when the system parameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the2.7order system. According to the stability theory of a fractionalorder linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchronization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7order system. The obtained experiment results accord with the theoretical analyses,which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

15.

A hyperchaotic system stabilization via inverse optimal control and experimental research





杨宁宁 刘崇新 吴朝俊《中国物理 B》,2010年第19卷第10期


In this paper, some basic dynamical properties of a fourdimensional autonomous hyperchaotic system are investigated by means of Poincar′e mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this fourdimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.

16.

Adaptive synchronisation of fractionalorder chaotic systems





张若洵 杨世平《中国物理 B》,2010年第19卷第2期


A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractionalorder chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractionalorder chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

17.

Synchronization of the fractionalorder generalized augmented Lii system and its circuit implementation





薛薇 ;徐进康 ;仓诗建 ;贾红艳《中国物理 B》,2014年第6期


In this paper, the synchronization of the fractionalorder generalized augmented Lti system is investigated. Based on the predictorcorrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractionalorder system and find that a fourwing chaotic attractor exists in the system when the system pa rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7order system. According to the stability theory of a fractionalorder linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

18.

PhotodiodeBased Chua＇s Circuit with Light Controllability





NAM Sang Guk NGUYEN Van Ha SONG Hanjung《中国物理快报》,2014年第6期


We present a photodiodebased Chua＇s chaotic circuit that is controllable by light. The proposed circuit consists of an inductor, two passive capacitors, a photodiodebased variable resistor, and a positive feedback trans conductor with negative nonlinearity. The chaotic dynamics of the circuit were verified by using the simulation program with integrated circuit emphasis analysis using the 0.35 #m complementary metaloxidesemiconductor process parameters. The gain results （such as the time waveform~ frequency analysis, threedimensional attractor, bifurcation and Lyapunov exponents diagrams） confirm that the chaotic behavior of the circuit could be controlled by light intensity via the photodiodebased variable resistor.

19.

Static and adaptive feedback control for synchronization of different chaotic oscillators with mutually Lipschitz nonlinearities





Muhammad Riaz Muhammad Rehan KeumShik Hong Muhammad Ashraf Haroon Ur Rasheed《中国物理 B》,2014年第11期


This paper addresses the control law design for synchronization of two different chaotic oscillators with mutually Lipschitz nonlinearities. For analysis of the properties of two different nonlinearities, an advanced mutually Lipschitz condition is proposed. This mutually Lipschitz condition is more general than the traditional Lipschitz condition. Unlike the latter, it can be used for the design of a feedback controller for synchronization of chaotic oscillators of different dynamics. It is shown that any two different Lipschitz nonlinearities always satisfy the mutually Lipschitz condition. Applying the mutually Lipschitz condition, a quadratic Lyapunov function and uniformly ultimately bounded stability, easily designable and implementable robust control strategies utilizing algebraic Riccati equation and linear matrix inequalities, are derived for synchronization of two distinct chaotic oscillators. Furthermore, a novel adaptive control scheme for mutually Lipschitz chaotic systems is established by addressing the issue of adaptive cancellation of unknown mismatch between the dynamics of different chaotic systems. The proposed control technique is numerically tested for synchronization of two different chaotic Chua＇s circuits and for obtaining identical behavior between the modified Chua＇s circuit and the R6ssler system.

20.

A new Rosslor hyperchaotic system and its realization with systematic circuit parameter design 被引次数：1





王光义 何海莲《中国物理 B》,2008年第17卷第11期


Based on two modified Rosslor hyperchaotic systems, which are derived from the chaotic Rosslor system by introducing a state feedback controller, this paper proposes a new switched Rosslor hyperchaotic system. The switched system contains two different hyperchaotic systems and can change its behaviour continuously from one to another via a switching function. On the other hand, it presents a systematic method for designing the circuit of realizing the proposed hyperchaotic system. In this design, circuit state equations are written in normalized dimensionless form by rescaling the time variable. Furthermore, an analogous circuit is designed by using the proposed method and built for verifying the new hyperchaos and the design method. Experimental results show a good agreement between numerical simulations and experimental results.
